Centripetal Force Calculator
Calculate centripetal force for circular motion. Solve for force, mass, velocity, or radius using the formula F = mv²/r.
What is Centripetal Force?
Centripetal force is the inward force that keeps an object moving in a circular path. It always points toward the center of the circle, which is why it is called centripetal (meaning "center-seeking" in Latin). Without centripetal force, an object would continue moving in a straight line tangent to the circle instead of following a curved path.
The formula for centripetal force is F = mv²/r, where F is the centripetal force in newtons (N), m is the mass in kilograms (kg), v is the tangential velocity in meters per second (m/s), and r is the radius in meters (m). The force can also be expressed in terms of angular velocity as F = mω²r.
Centripetal force is encountered in many everyday situations. A car turning a corner requires friction between the tires and the road to provide the centripetal force. Roller coasters use centripetal force to keep riders safely in their seats during loops. Satellites in orbit around Earth are kept in their circular paths by the gravitational force acting as the centripetal force. Even a ball swung on a string requires tension in the string to provide the necessary centripetal force.
How to Use the Centripetal Force Calculator
This calculator solves for any of the four variables in the centripetal force equation. Select which variable you want to calculate from the dropdown menu, then enter the known values. The calculator will automatically compute the result and display it in real time.
- Solve for Force: Enter mass, velocity, and radius to find the centripetal force required to maintain circular motion.
- Solve for Mass: Enter force, velocity, and radius to determine the mass of the object.
- Solve for Velocity: Enter force, mass, and radius to find the tangential velocity.
- Solve for Radius: Enter force, mass, and velocity to calculate the radius of the circular path.
The calculator also displays the centripetal acceleration and angular velocity, providing a complete picture of the circular motion parameters.
Centripetal Force Formula Derivation
The centripetal force formula is derived from Newton's second law of motion, F = ma, combined with the centripetal acceleration formula, a = v²/r. By substituting the centripetal acceleration into Newton's second law, we get F = m(v²/r) = mv²/r.
Frequently Asked Questions
What is the difference between centripetal and centrifugal force?
Centripetal force is a real inward force that acts toward the center of a circular path. Centrifugal force is an apparent outward force experienced by an object in a rotating reference frame. While centripetal force is required for circular motion, centrifugal force is a fictitious force that appears only in non-inertial reference frames.
Can centripetal force do work on an object?
No, centripetal force does no work on an object in uniform circular motion because the force is always perpendicular to the direction of motion (the velocity vector is tangent to the circle, while the force points toward the center). Since work is force times displacement in the direction of the force, and there is no displacement in the radial direction, the work done is zero.
What happens if centripetal force is removed?
If the centripetal force is removed, the object will continue moving in a straight line tangent to the circular path at the point of release, following Newton's first law of motion. This is why a ball swung on a string flies off in a straight line when the string is released.
How does centripetal force relate to g-forces?
Centripetal force is directly related to g-forces. One g equals 9.81 m/s² of acceleration. An object experiencing a centripetal acceleration of 19.62 m/s² is experiencing 2 g's. The centripetal force required for this is F = m × (2g), meaning the apparent weight doubles. This is why roller coasters and fighter jet maneuvers are described in terms of g-force.
What is the maximum centripetal acceleration a human can withstand?
Untrained individuals can typically withstand about 5 g's (49 m/s²) of centripetal acceleration before losing consciousness due to blood pooling. Trained fighter pilots with g-suits can withstand up to 9 g's (88 m/s²) for short periods. The corresponding centripetal force for a 70 kg person at 5 g's would be approximately 3,430 N.
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